Using a seven$-$segment LED display and a $4-$bit BCD decoder, design a circuit that generates a visual output representing input numbers $0$ to $9.$ In your design, make sure to show the following components:

a$)$ A block diagram of the input and output circuitry

$[2$ marks$]$

b$)$ A truth table showing the decimal and binary input characters and the corresponding lit LED scgments of the output display.

$[4$ marks$]$

c$)$ Karnaugh map representation of the $"a","$b$","$c$"$ and $"d"$ columns of the sevensegment output display.

$[8$ marks$]$